List of top Questions asked in KEAM

The number of S-S bonds and the number of lone pairs in S₈molecule,respectively,are:

In an oil drop experiment, 'n' numbers of electrons are stripped from an oil drop to make it positively charged. A vertical electric field of magnitude 4.9x10¹⁴ N/C is applied to balance the force due to gravity on the oil drop. If the mass of oil drop is 80 μg,the value of 'n' will be:(Take g =9.8 m/s² and charge of an electron = 1.6 x 10^-19 C)

A planet has an escape speed of 10km/s,The radius of the planet is 10,000km. The acceleration due to gravity of the planet at its surface is:

The number of solutions of the equation \( \dfrac{1}{2}(x^3+1)=(2x-1)^{⅓}\) is

The domain of the real valued function \(f(x)=\dfrac{√(x2−7x+6)}{√(x2−4+1)}\) is

A system of ideal gas undergoes a thermodynamic process in which the initial pressure and volume are equal to the final pressure and volume. Let △Q is the heat supplied to the system,△W is the work done by the system and △U is the change in internal energy. The correct option is:

Let \(f:R→R\) be a function defined by \(f(x)=x^2+9\).The range of \(f \) is

A projectile is thrown at a speed V and at an angle with the horizontal. If the speed at its maximum height is \(\frac{V}{3}\),then the value of tan θ is:

Suppose P is the point on the line joining \((-9,4,5)\) and \((11,0,-1)\) that lies closest to the origin O. Then \(|OP|^2\) equals to?

Suppose the line joining distinct points P and Q on \((x-2)^{2}+(y-1)^{2}=r^{2}\) is the diameter of \( (x-1)^2+(y-3)^2=4\).The value of r is

An ideal gas is kept in a closed container. If the temperature is doubled and the volume of the container is reduced to half, the gas pressure is:

A series LCR circuit consists of a variable capacitor connected to an inductor of inductance 50 mH,resistor of resistance 100 Ω and an AC source of angular frequency 500 rad/s. The value of capacitance so that maximum current may be drawn into the circuit is:

Let \(k\) be a real number such that \(\sin \dfrac{3π}{14} \cos \dfrac{3π}{14} = k \cos \dfrac{π}{14}\).Then the value of \(4k\) is

Find the effective resistance between points A and B. Each resistance is equal to R.

Suppose a line parallel to \(ax+by=0\) (where \(b≠0\))intersects\( 5x-y+4=0\) and \(3x+4y-4=0\) ,respectively at P and Q. If the midpoint of PQ is \((1,5)\),then the value of \(\dfrac{a}{b}\) is

A biased die is rolled such that the probability of getting k dots,1≤k≤6, on the upper face of the die is proportional to k. Then the probability that five dots appear on the upper face of the die is

In a Young's double slit experiment which of the following statements is NOT true?

\(\text{The value of } cosec20°tan60°-sec20° \text{is }\)

The area of the region in the first quadrant which is above the parabola \(y = x^2\) and enclosed by the circle \(x^2 +y^2 = 2 \) and the y-axis is

The area of the region in the first quadrant enclosed by the curves\( y=√x,y=-x+6 \)and the x-axis is

The kinetic energy of a particle of mass m₁ moving with a speed V is same as the kinetic energy of a solid sphere of mass m₂rolling on the plane surface. If the speed of the Centre of the sphere is also V,then m₁/m₂ is:

For \(i=1,2,3,4\), suppose the points\((\cosθi,\secθi)\) lie on the boundary of a circle,where \(θi∈[0,\frac{π}{6})\) are distinct. Then \(\cosθ_1\ \cosθ_2\ \cosθ_3\ \cosθ_4\) equals

A thin convex lens of refractive index 1.5 has a focal length of 10 cm in air. When the lens is immersed in a fluid,its focal length becomes 70 cm. The refractive index of the fluid is

Car P is heading east with a speed V and car Q is heading north with a speed \(\sqrt{3}\). What is the velocity of car Q with respect to car P?

For any \(n≥0\) the value of \(\sum_{r=0}^n \dfrac{(4r+3).(nC_r)^2}{(2n+3)}\) is